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Question: Find the value of sec 20 - 3cosec 20.


A ) 0
B ) -4
C ) 1
D ) 4

Steps to derive

1 sec 20 - 3cosec 20 = 1cos 20-3sin 20

2 = sin 20 -3cos 20sin 20cos 20

3 = 2×(12sin 20-32cos 20)12×(2sin 20cos 20)
 [Multiply and divide the numerator and the denominator by 2.]

4 = 4 × (cos 60sin 20-sin 60cos 20)sin 40

5 = -4 × (sin 60cos 20-cos 60sin 20)sin 40

6 = -4 sin(60-20)sin 40
 [Use sin Acos B - cos Asin B= sin (A - B).]

7 = -4 × sin 40sin 40 = -4



Hence the right answer is Option B

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